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Hi David,

This is a fascinating attempt at proving the Consequence Argument. Thanks for sharing it and for your helpful summary of Pruss’s argument. Let me take a stab at what I think is could be a problem in the argument.

The principle called Weaken (page 2&3 on your summary and page 4 in Pruss’s paper) does a lot of work in Pruss’s arguments. As I see it, one problem for this principle is that the context in which Weaken is proved assumes p and q are propositions describing *events*. Lewis-Stalnaker semantics of counterfactuals of course explicitly assumes p and q are restricted to events in this way. When Weaken is deployed later in the proofs of the CA, however, p is no longer a proposition describing an event, but rather a proposition describing an event (in the remote past) *conjoined with a description of the laws of nature* (see for example line 4 of the proof of the CA on page 4 of your summary, or line 2 of the proof on page 4 of Pruss’s paper). Switching the nature of p in this way makes a huge difference.

To see why this switch is problematic, consider what Lewis himself repeatedly says about how we evaluate counterfactual conditions. What we do, roughly, is look at whether the consequent of the conditional is true in worlds that are most similar to the actual one but for a *local miracle* that makes the antecedent of the conditional true. These are worlds in which the laws of course will be slightly different from the actual world to accommodate the local miracle. Lewis even explicitly discusses these ideas, and embraces the “laws are slightly different” approach, in the context of discussing the CA in his famous paper “Are we free to break the laws?”.

This “local miracle/laws are slightly different” approach is not consistent with Weaken when we allow the relevant proposition p to describe some event *conjoined with a description of the laws of nature*. This is equivalent to holding fixed the laws of nature in the relevant evaluated world, which is precisely what Lewis’s “local miracle/laws are slightly different” approach says we should not do.

Do you think this criticism has any merit?

David, you stated: “If correct, this result strengthens the incompatibilist position with respect to free will and determinism, since now the only alternatives open to the compatibilist are either to deny the fixity of the past, or to deny the fixity of the laws of nature.”

Perhaps there is another alternative open to the compatibilist, wherein the compatibilist believes that new forces are an emergent property of life, and those forces add together with the “laws of nature” thereby affecting the path forward and creating free will.

I just don’t know if we want to say the *only* alternatives open to the compatibilist are…

I want to restate my issue with Pruss’s paper and provide another more formal take on what I see as a potential issue.

Once again, I think the key to Pruss’s argument is the principle he calls “Weaken”.

Let “>” be the counterfactual conditional.

“Weaken” says that from 1) p > q; and 2) necessarily(q → r), then we can infer p > r

Weaken seems innocuous when p, q, and r are all propositions describing *events*: Were I to press the trigger, I’d shoot a bachelor; necessarily, if I shoot a bachelor then I shoot an unmarried man; so were I to press the trigger, I’d shoot an unmarried man. Indeed Lewis/Stalnaker semantics for counterfactuals apparently insists that the relata for “>” must be events. Call a version of Weaken restricted this way Weaken-Restricted. There is a looser version of Weaken that allows things such as propositions describing the laws of nature to enter as relata of the counterfactual conditional. Call this version Weaken-Loose. Weaken-Loose is problematic because it produces highly counterintuitive results.

Here is an example:

Let s be the agent
Let p be a proposition describing the past and deterministic laws of nature
Let q be a true proposition about the present, “My hand rests on the table”
Let a = “I raise my hand”

1. does(s,a) > not q
2. necessarily(not q → not p)
3. does (s,a) > not p (by Weaken-Loose)

Lewis’s paper “Are we free to break the laws?” is basically an extended argument for why this pattern of reasoning is problematic. So at the very least, Weaken-Loose needs a good argument in its defense, but none is offered in Pruss’s paper.

Pruss is absolutely right that Beta-2 follows from Weaken, and this is indeed an important insight. But we must be careful. Since there are two versions of Weaken, there are two versions of Beta-2 that can be proved. The one he needs is Beta-2-Loose that depends on Weaken-Loose, since the CA requires one of the arguments of Beta-2 to be a proposition describing the past and laws of nature (rather than an event). However, it is precisely this version that is highly problematic for the reasons Lewis identifies. Beta-2-Restricted (which depends on Weaken-Restricted) on the other hand can’t be used to prove the CA.

David et. al.

Fascinating stuff.

These matters are complex and delicate. I just want to make a small point here. If we interpret "Free Will" as requiring freedom to do otherwise (regulative control, to return to terminology that Joshua might find of interest), it is correct that a proof of Beta narrows the options for a compatibilist in the way indicated by David. But if "Free Will" can refer to acting freely (guidance control), or perhaps the freedom required for moral responsibility (whatever that is), then there is a further option available for the compatibilist: Semicompatibilism.

Of course David also has legitimate worries about the Frankfurt Cases (a matter about which we respectfully disagree). I simply here wanted to mark this possibility for compatibilists. The power and plausibility of the arguments on both sides of the Consequence Argument set up what I've called Dialectical Stalemates, and have inclined me toward Semicompatibilism.

What does “event e would falsify proposition p” mean in this argument? Suppose we say what Lewis said in AWFTBTL: e falsifies p iff necessarily (if e occurs, p is false). Suppose determinism is true and that my situation is non-pathological. Lewis thinks I could have raised my arm even though I didn’t. Premise 3 looks good: the arm-raising event wouldn't have falsified L because it’s possible that that event occurs even if L is true—the past just has to be a little different. Premise 2 looks good: the arm-raising event wouldn't have falsified P because it’s possible that the past is exactly the same and that the arm-raising event occurs—the laws just have to be different for that to happen. But I can raise my arm and the arm-raising event falsifies the conjunction, i.e. necessarily (if the arm-raising event occurs, either P or L is false). So the inference from (2) and (3) to (4) is an inference Lewis would reject, if we operate with his definition of an event falsifying a proposition.

Thanks for posting this, David.

Dr. Sripada:

Lewis does not limit his account of counterfactuals to reports of events. And rightly so. After all, we want to be able to ask questions like "If gravitation had an inverse cube law, could there be stable orbits?" where the antecedent is not the report of an event. So Lewis at least is committed to Weaken in full generality.

By the way, the most plausible counterexamples to Weaken involve impossible antecendents. Weaken (plus the uncontroversial "were p to hold, p would hold") implies that every counterfactual with impossible antecedent is true (Lewis embraces the conclusion). So one might want to restrict Weaken to cases where the antecedent is possible. Fortunately, my argument can be formulated in such a way that Weaken is applied only in the case of possible antecedents.

Hi John,

When saying that this result strengthens the incompatibilist’s position with respect to free will and determinism, I meant, of course, 'free will' in the sense of freedom to act otherwise. I was not concerned with the incompatibility between moral responsibility and determinism. Since freedom to do otherwise is a legitimate sense of acting freely, Pruss’s result does narrow the options of a compatibilist about determinism and freedom to do otherwise.

Semicompatibilism is a position which, though agreeing that determinism is incompatible with freedom to act otherwise, insists that determinism is compatible with moral responsibility. Hence, Pruss's result seems to be consistent with your Semicompatibilism, and possibly can be even taken to strengthen it.

Professor Fischer:

There are indeed subtle issues here. I think we can separate my version of the consequence argument into three controversial premises, and some uncontroversial stuff. The controversial stuff is:

1. For all p: if Np (as defined in my paper), then no one is free with respect to p
2. N(past and laws)
3. Weaken

Lewis then denies 2. As I understand your view, it's a denial of 1, at least for the kind of freedom that responsibility requires.

We can break up 1 into two premises:
1a. If Np, then no one ever has a choice about whether p.
1b. If no one ever has a choice about whether p, then no one is free with respect to p.

I am interested whether you take yourself to be denying 1a or 1b.

If I were a compatibilist, I think I would deny 1a (and also express some reservations about the exact formulation 1b).

Thanks for the clarification Alexander. I was applying a restriction that the relevant counterfactuals are used in the analysis of causal relations, but I see now this restriction is simply unwarranted. So I concede that Weaken is quite plausible in an unrestricted form, and as you show, beta-2 follows quickly.

I have recently been attracted to a conditional analysis of can, where “I can do x” means something like “I would do x if certain motivational conditions were to obtain”, or close cousins of this approach that use possible worlds directly (i.e., Lewis-Kratzer-style approaches). I used to think this conditional analysis was a direct challenge to transfer principles like beta-2, and I wouldn’t necessarily need to challenge the fixity of the past/laws. Not that I endorse the latter. Its just that beta-2 seemed like it should be the main target for defenders of the conditional view. I am increasingly convinced by your proof that defenders of the conditional analysis should outright concede beta-2. They should instead focus, like Lewis does, on how the conditional analysis of “can” (or its cousins), appropriately understood, lead to rejecting the fixity of the laws.

Chandra (and others),

I have never understood how denying the fixity of the laws a la Lewis can help secure free will if the denial simply amounts to the claim that the laws could have been different than they actually are (i.e., they are/were different in some not so distant world). The issue is whether the laws are fixed with respect to the actual world--i.e., the world we inhabit. Telling me I am free because the laws could have been different than they actually are seems like a pretty flimsy ground for free will and responsibility. Isn't it tantamount to the suggestion that I am free because miracles exist in some other world? If the miracles aren't here to ground my free will in this world, then they're no help to me at all. At most, you have shown that my counterparts in possible worlds were able to do things not available to me in this world! I take it I am clumsily misunderstanding something here. So, I figured this would be a good forum to seek some clarification!

Thomas, I definitely get that it seems weird to think the goings on in nearby possible worlds, especially in regards to their laws, matters for my powers and abilities in this world. But to people who raise this issue, especially incompatibilists, consider this sort of tu quoque argument: Precisely the same problem you raise arises for dispositional properties in non-agentive contexts. Suppose an analysis of dispositions that invokes counterfactual conditionals is correct (and it is still the best game in town I think), and our laws are deterministic, and in deterministic worlds objects still have their (general) dispositional properties (even PvI believes this). Then it is the case that the salt’s being soluble depends on the fact that in a nearby world in which a law-breaking divergence miracle occurs, the salt is immersed in a liquid and it dissolves. This sounds just as weird as the weirdness you pointed out. But the weirdness is something that everyone, compatibilists and incompatibilists alike, must swallow. Does this seem right?


Granted, Lewis's point can't just be that the laws could have been different; somehow the possibility in question must be up to the agent or matched to the agent's actions in a suitable sense.

But to your more general point, facts about other possible worlds do bear on necessity or fixity characteristics in this world. So, I'm wearing a blue shirt. But I could have worn a red shirt. This is shown (arguably) by the fact that I or my counterpart am wearing a red shirt in another possible world (suitably related to, or accessible from, this world). The fact about the other world shows that in this world there is a certain sort of possibility.


Yes, right, we are in agreement. The acceptance of the CA is completely consistent with (though not required by) Semicompatiblism. (I was just highlight this for the sake of the blog.)


I don't think I accept 1b, since one can be "free with respect to" an action even if one does not have freedom to do otherwise, on my approach. That is, one can act freely (exhibit guidance control) without being free to do otherwise (possess regulative control).

David is correct that as a Semicompatibilist, I could accept the Consequence Argument fully. I am an actual-sequence theorist of moral responsibility. But feel the force of the argument, but I also feel the force of Lewis-style objections.

I'm curious why Lewis denies

(2) N(L&P)

because I deny it too, and I wonder if it's for the same reason. In particular, Pruss claims in the paper that

(b) there is no choice about the laws.

Note that when Pruss defines the past P, he is careful to specify the PRE-HUMAN past. This is presumably because, if we included the human past too, then we would have to beg the question against compatibilism when we assert (2). After all, on compatibilism, the human past includes choices we made.

But it seems to me that in order for (2) to be true, we need to make an analogous restriction to the laws L. On the assumptions of determinism and compatibilism, if we had made different choices then the laws describing them would have been different. In that sense NL, and similarly N(L&P), would both be false.

In fact, I don't even think we need determinism to deny N(L&P), because it should be false as long as at least SOME of our choices are regular enough to be described by laws.

On the other hand, if we restrict L sufficiently to make N(L&P) demonstrably true on determinism, then it would no longer be obvious that determinism would require

(1) []((L&P)->r)

to hold for a given choice r, or indeed ANY choice r.


You said: "The fact about the other world shows that in this world there is a certain sort of possibility." Right. I get that's how the view goes. Here's another way of stating my unease: On this view, I can do only that which I actually do. The only sense in which it means to say *I* could have done otherwise than I do at any moment is to say that *my counterparts* on near (and even distant) worlds behaved differently than *me* under varying degrees of similarity of circumstance. But I only want to be held desert-based responsible for beliefs, attitudes,, and behaviors that *I* could have *actually* avoided given the past and the natural laws that shaped how my life unfolded. On the view we're discussing, it seems instead that *I* am held hostage in the actual world to the miracles unfolding in the lives of my counterparts on near and distant worlds. I take it this is part of the weirdness Chandra and I were discussing. He seems to think this is a bitter pill all parties to the debate have to swallow. I need more time to think about that, so stay tuned. For now, I just wanted to take another quick stab at explaining why the "miracles matter" view about free will and responsibility seems puzzling (at least to someone who hasn't read the Lewis stuff on free will in an embarrassingly long time).


I grant that local-miracle compatibilism, as well as multiple-pasts compatibilism, and Lewis-style compatibilism (which is a melange of both), are "weird" in certain ways. That's why I'm not inclined to be a classical compatibilist.

But note: I'm wearing a blue shirt. But in another p.w., my counterpart is wearing a red shirt. Acc. to Lewis, this shows that I "actually" do have the possibility of wearing a red shirt. Better: it shows that it is really and truly possible that I wear a red shirt. Ditto for laws, etc. I don't think this in itself is the problem. The problems however are there, and you are right to worry about them.

Doesn't Np entail that "can" is anti-compatibilist?

Let s be the agent
Let p be a proposition describing the past and deterministic laws of nature
Let q be a true proposition about the present, “My hand rests on the table”
Let a = “I raise my hand off the table”

1. Np
2. [](p --> q)
3. Nq
4. (x)(A) {Can(x,A) --> ~[Does(x,A) > ~q]}
5. (x)(A) {[Does(x,A) > ~p] --> ~Can(x,A)}
6. [Does(s,a) > ~q] --> ~Can(s,a)
7. ~Can(s,a)

(4 is from 3 and the definition of N, and corresponds to the 4 in David's version of the proof.)

So the agent with his hand on the table can't raise his hand.

Isn't this an RAA of Np (or of N(P&L) as it's also written earlier in this discussion)?

Hi James,

You say,

"Perhaps there is another alternative open to the compatibilist, wherein the compatibilist believes that new forces are an emergent property of life, and those forces add together with the “laws of nature” thereby affecting the path forward and creating free will."

DW: Wouldn't what you say also support a libertarian position?

You say:

"I just don’t know if we want to say the *only* alternatives open to the compatibilist are..."

I think, I DO know! But how about: "As far we currently can see, the only alternatives open to the compatibilist are..."


I believe it's wrong to think of possible worlds as other worlds. Possible worlds are this world, as it might be (or might have been). And the "might" is epistemic, not metaphysical. It's convenient to think of them as other worlds, but ultimately wrong.

The fact is that you don't know what P and L are in any detail. The fact is, you don't know whether P and L entail q (some outcome you'd like to avoid (for moral reasons)). So far as you know, it is possible for you to raise your hand off the table. That doesn't mean that there's some other world somewhere where someone who looks and thinks like you raises his hand off the table; it means that P and L might be such that you (the you in this, the actual world) will raise your hand off the table.

And the really amazing thing is that P and L are such that it's up to you whether you raise your hand off the table. And that's not making any sort of claim about the nature of P and L; it's just a claim about what "up to you" means.

And since it is up to you, it's perfectly reasonable to hold you responsible for that action and any of its consequences that you should be aware of.

@ Chandra:

It sounds to me like you think that Lewis endorsed some sort of conditional or counterfactual analysis of ability. Do you think he endorsed a view of that kind in AWFTBTL? I can't tell how many other people attribute that kind of view to Lewis, but I think he endorsed no such view in that paper. In fact, I think the argument of the paper does not depend on his having any account of ability whatsoever and I do not think he offers one as an extra goodie. He does offer weak and strong definitions of the quasi-technical idiom 'being able to render a proposition false' in terms of counterfactuals. But that definition uses—and so does not analyze—the notion of an agent's being able to perform an action.

Also, on the dispositions analogy: It may well be true that there is an equivalence between disposition ascriptions and certain (sets of) counterfactuals or (sets of) statements about how an object performs in a range of possible situations. But you can accept that there are some magic bi-conditionals along these lines without thinking that they analyze dispositions. So I'm not really sure that everyone "must swallow" these claims. It doesn't seem crazy to me to think that the counterfactual truths are not more fundamental than the dispositional truths. Maybe that's wrong. But, after all, you appear to admit that the solubility-analyzed-as-dissolving-counterfactual claim sounds weird which is some evidence that it's wrong.

@ Ben: you asked why Lewis denies N (P & L). I think I addressed it in my previous comment. The answer is (where we interpret 'N' strongly): even if determinism is true, I can raise my arm and, were I to do so, the arm-raising event (my action) would occur and its occurrence necessitates the falsity of (P & L). His denial of N (P & L) is, I think, an artifact of his definition of 'e renders P false'. Suppose we operate with a different definition: e renders p false iff p is false in virtue of the fact that e occurred. Presumably, then, the Lewisian-compatibilist should accept that N (P & L) (interpreted strongly). For it does not seem that the fact that I raised my arm explains the falsity of (P & L)at the world where my arm goes up, even if the former fact necessitates the falsity of the latter.

Hi John,

Just a clarification. You say that "The acceptance of the CA is completely consistent with (though not required by) Semicompatiblism."

If *freedom to do otherwise* is not inconsistent with determinism, then what does 'semi' in semicompatibilism' denote?

But perhaps you meant that the acceptance of *CA*(=Consequence Argument)is not required by Semicompatibilism. If so, would you still maintain this, given A.P's exciting result, understanding unavoidability in terms of Pruss's M-operator + replacing van Inwagen's Beta-rule by Pruss's Gamma-2 rule?

Also, would the acceptance of what you call 'The Basic Argument for the incompatibility of determinism and freedom to do otherwise' be required by semicompatibilism?


Lewis denies N(L and P) because he thinks that, assuming determinism in the actual world w0, then in the nearest world w1 where he acts otherwise (I am simplifying by assuming there is a nearest), there is a "small miracle" in his brain prior to his choice, which is a deviation from this world's laws L. Thus, L is false at w1. In fact, it looks like Lewis actually denies NL.

Lewis's view is this: My acting otherwise wouldn't constitute or cause a violation of L, but were I to act otherwise, L would be false.

@Nate: I agree, I don’t think Lewis provides an account of ability in AWFTBTL. Now, there is the so-called "Lewis-Kratzer" view of modals including "can" and abilities, named I think because it has a kind of source in certain remarks Lewis made in various papers. One might think this represents Lewis’s view of "can" or abilities, but I suspect this might be a leap. If it were Lewis’s view, then in the end, I don’t think it is much that different than the counterfactual approach in terms of weirdness. On both approaches, we attribute abilities ultimately in terms of goings on at other possible worlds (including one’s where the laws are different).

I think your more basic point that we aren’t all obligated swallow weirdness quite yet because some non-counterfactual/non-modal analysis of “can”/ability might be right. This point is well taken.

Hi David,

"Semicompatibilism" denotes the view that moral responsibility is compatible with causal determinism, apart from whether causal determinism is compatible with freedom to do otherwise. As such, the doctrine takes no stand on whether causal determinism is compatible with freedom to do otherwise. Qua proponent of Semicompatibilism, I take no stand on this issue. In my view, this is an important virtue of Semicompatibilism (and actual-sequence theories in general): one can sidestep these extremely delicate and difficult issues.

However, the total package of JMF's views does include incompatibilism about causal determinism and freedom to do otherwise. I do accept the Basic Argument for incompatibilism, employing Ginet's principle: our freedom is the power to add to the given past, holding fixed the laws of nature.

But I don't think this argument is airtight and knockdown. I don't think ANY argument for incompatibilism is. Yes, I accept the Basic Version of the argument, but I don't think any rational agent would have to accept it, simply qua ratiional agent (or any such thing).

I note that Alexander Pruss's result is interesting, and I'll think about it more carefully. But I also wish to highlight the fact that I do not think ANY modal transfer principle is required for the Consequence Argument. Further, it is clear that such a principle is not sufficient, since one can deny the fixity of the past and/or laws (suitably interpreted).

The past is broken. By which I mean, it's not fixed. Bad physics leads to philosophical error. http://plato.stanford.edu/entries/determinism-causal/#DetHumAct ; and see Jenann Ismael's talk “On Why We See the Past as Fixed and the Future as Something We Can Bring About by Will: The View Through the Lenses of Physics” (53:52 – 1:38:51) at http://www.freewillandscience.com/wp/?page_id=450

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